How do I calculate the Credible interval of the effect size? (Bayesian framework)

Question

I use R. I have a linear mixed model and I use its output to estimate my posterior distribution (with uninformative priors) using the function sim.

I calculate the effect size between different subgroup as differences between the fitted values. Shall I use the same criteria also for the credible intervals (CrI)?

Example: Subgroup1 has (-0.11, 0.01, 0.13) as lower, fit and upper estimates (95% CrI) Subgroup2 has (0.09, 0.26, 0.42) as lower, fit and upper estimates (95% CrI)

The effect size is for me 0.25, what about its CrI? Again just the difference?

Answer 1

Rather than subtracting 0.01 from 0.26, you should be using all of the posterior estimates from which you can obtain the posterior effect size estimate (mean/median) and interval. For instance, generate thousands of estimates for each coefficient, generate a new variable with the difference between the entire posterior distribution of two coefficients, and then use the quantile function to obtain an equal tailed credible interval.